The height of the AM triangle ABC divides its side into segments BM and MC find the length of the MC

The height of the AM triangle ABC divides its side into segments BM and MC find the length of the MC if AB is 10 ^ 2cm. BC is equal to 26cm. angle B is 45 degrees

Since the segment AM is the height of the triangle ABC, then the triangle ABM is rectangular, and since one of its angles is equal to 450, the legs of this triangle are equal. AM = BM, then, by the Pythagorean theorem, AM ^ 2 + BM ^ 2 = AB ^ 2.

2 * BM ^ 2 = AB ^ 2.

BM ^ 2 = AB ^ 2/2 = 100 * 2/2 = 5 * 100.

BM = 10 cm.

Then MS = BC – BM = 26 – 10 = 16 cm.

Answer: The length of the MC segment is 16 cm.